For the function f(x)=(3+x)/(4x-9), find f^(-1)(x). Answer: f^(-1)(x)=

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For the function  f(x)=(3+x)/(4x-9), find  f^(-1)(x). Answer:  f^(-1)(x)=

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Replace with y: To find the inverse function, f^(-1)(x), we need to switch the roles of x and y in the original function and then solve for y. Let's start by replacing f(x) with y for clarity. y = (3 + x) / (4x - 9)Switch x and y: Now, switch x and y to find the inverse function. x = (3 + y) / (4y - 9)Multiply by (4y - 9): Next, we need to solve for y. To do this, we'll multiply both sides of the equation by (4y - 9) to get rid of the fraction. x * (4y - 9) = 3 + yDistribute x: Distribute x on the left side of the equation. 4xy - 9x = 3 + yMove y to left: Now, we want to get all the terms with y on one side and the constants on the other. Let's move y to the left side by subtracting y from both sides. 4xy - y - 9x = 3Factor out y: Factor out y on the left side of the equation. y(4x - 1) = 3 + 9xDivide by (4x - 1): Now, divide both sides by (4x - 1) to solve for y. y = (3 + 9x) / (4x - 1)Inverse function found: We have found the inverse function. Therefore, f^(-1)(x) is: f^(-1)(x) = (3 + 9x) / (4x - 1)

For the function $f(x)=\frac{3+x}{4 x-9}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$

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For the function f(x)=3+x4x−9 f(x)=\frac{3+x}{4 x-9} f(x)=4x−93+x​, find f−1(x) f^{-1}(x) f−1(x).\newlineAnswer: f−1(x)= f^{-1}(x)= f−1(x)=

For the function $f(x)=\frac{3+x}{4 x-9}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$